Extension of the app is also like a main application hence required dedicated setup of bundle id, signing cert and provisioning profile. It seems, your extension is not provided with above configurations. Please check.
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Though both profiles looks same, they are different w.r.t to the purpose and distribution. Both profiles allows to confine to install on only selected/ registered devices only. But the purpose of development profile is for development and debugging purpose by using dev signing cert where as adhoc profile is for distribution purpose such as to adhoc testers and TestFlight distribution with signing distribution certificate.
As the type of signing certificate is different in both cases, adhoc profile stands similar to Appstore profile with distribution certificate and features such as Push notifications pointing to APNS prod instance can be tested before releasing app to store.